This paper presents a rigid-plastic finite element method for orthogonal cutting process by adopting Lagrange method. The rigid-plastic FEM analysis model is established and the rigid-plastic FEM analysis toolkit was developed. Meanwhile, two relevant key problems are discussed systematically, including the rule of chip-workpiece separation and the criterion of tool-chip separation. At last, a simulation example of planing an aluminium alloy (ZL-301) workpiece was conducted. The effects of the cutting stroke, the tool rake angle and the friction coefficient on chip were observed. The numerical simulation results have a good agreement with their experimental ones. It is indicated that the presented FEM model and algorithm are efficient and correct.